[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85544-en":3,"doc-seo-85544-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85544,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","An Approximate Graph Elicits Detonation Lattice","This study develops a novel graph-theory algorithm for precise segmentation and quantitative measurement of detonation cells from 3D pressure traces, producing detonation lattices. It addresses shortcomings of manual workflows and brittle 2D edge detection when applied to irregular 3D cellular structures. A training-free segmentation model is validated on synthetic datasets (2% error), then evaluated on 3D simulation data using statistical and joint probability-density measures. Results indicate oblong cells aligned with the wave-propagation axis with 17% deviation, with larger volume dispersion reflecting cubic amplification of linear variability, while complex patterns remain challenging to segment reliably.","arXiv :2603 . 16524v2 [ cs .CV] 13 Jul 2026  \nAn Approximate Graph Elicits Detonation Lattice  \nVansh Sharmaa,∗ and Venkat Ramana  \na Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109 -2102, USA  \nAbstract  \nThis study presents a novel algorithm based on graph theory for the precise segmentation and measurement of detonation cells from 3D pressure traces, termed detonation lattices, addressing the limitations of manual and primitive 2D edge detection methods prevalent in the field. Using a segmentation model, the proposed trainingfree algorithm is designed to accurately extract cellular patterns, a longstanding challenge in detonations research. First, the efficacy of segmentation phase on two synthetic datasets is evaluated with an error of 2% . Next, 3D simulation data is used to establish performance of the graph-based workflow. The results of statistics and joint probability densities show oblong cells aligned with the wave propagation axis with 17% deviation, whereas larger dispersion in volume reflects cubic amplification of linear variability. Although the framework is robust, it remains challenging to reliably segment and quantify highly complex cellular patterns. However, the graph-based formulation generalizes across diverse cellular geometries, positioning it as a practical tool for detonation analysis and a strong foundation for future extensions in triple-point collision studies.  \nNovelty and significance statement  \nDetonation cells are key features of canonical propagating waves, and are useful for understanding cellular instabilities. Currently, there is very limited work on methods for estimating cell sizes, with manual counting in two-dimensions being the common approach. Existing numerical approaches typically work with 2D data, require extensive manual intervention, or rely on 2D edge heuristics that lack robustness and applicability across 3D volumetric data. This work, to the best of the authors’ knowledge, is the first to present a generalized algorithm that automatically detects, segments, and quantitatively measures three-dimensional detonation cells using graph theory. The proposed method provides geometric structure of three-dimensional cells, vastly improving the ability to understand detonation structures. These findings will ultimately help improve practical detonation applications (rotating, pulse, oblique and standing detonation wave engines) .  \nKeywords: 3D Detonation; Soot Foil; Graph; Cell Classification; Cellular Detonation; Detonation Lattice; SAM Model  \n*Corresponding author.  \n1. Introduction  \nAs detonation-based devices [1] were pioneered in the early 1950s, soot foils emerged as a diagnostic tool to visualize the two-dimensional cellular imprint of triple-point trajectories and associated wavecollision points on the confining surface, to study intrinsic high-speed combustion and shock phenomena. These soot-coated substrates are placed along gaseous detonation channels that record triple-point tracks asthe wave propagates, producing a “cellular lattice”imprint of the detonation front. Despite widespread use, these techniques are inherently two-dimensional, sampling only wall-adjacent dynamics and missing the full 3D front morphology. This motivates techniques to map the soot-foil lattice patterns to a 3D volumetric representation with minimal human effort.  \nSeveral techniques have been developed to quantify the cellular pattern on 2D soot foils [2–6] . Shepherd et al. [7] proposed a PSD-based cell-size estimator coupled with edge detection, linking pattern periodicity to dominant spatial frequencies via 2D Fourier analysis. Subsequent workflows and software packages popularized this route but retained substantial manual tuning. Carter et al. [3] extracted directional gradients with manual input to overlay binary cell maps while Ng et al. [5] performed CH*-based extraction of soot-foil-like patterns and then measured λ (characteristic cell width) with t","cbCaiag1j9ASDjtr","https://ap.wps.com/l/cbCaiag1j9ASDjtr","pdf",7265024,2,1,10,"English","en",105,"# Introduction\n## Background: soot foils and 2D diagnostics\n## Prior work on 2D cell quantification\n## Motivation for 3D detonation lattice mapping\n## Graph-based perspectives on detonation structure","[{\"question\":\"What does the proposed method extract from the data?\",\"answer\":\"It automatically detects, segments, and quantitatively measures three-dimensional detonation cells, forming a detonation lattice representation from 3D pressure traces.\"},{\"question\":\"How is the algorithm validated in the study?\",\"answer\":\"Segmentation performance is evaluated on two synthetic datasets with an error of 2%, and the broader graph-based workflow is assessed using 3D simulation data with statistical and joint probability-density analyses.\"},{\"question\":\"What do the results indicate about detonation cell geometry?\",\"answer\":\"The findings show oblong cells aligned with the wave propagation axis with 17% deviation, while dispersion in volume reflects cubic amplification of linear variability.\"}]",1784204332,25,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"an-approximate-graph-elicits-detonation-lattice","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/an-approximate-graph-elicits-detonation-lattice/85544/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What does the proposed method extract from the data?","Question",{"text":75,"@type":76},"It automatically detects, segments, and quantitatively measures three-dimensional detonation cells, forming a detonation lattice representation from 3D pressure traces.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the algorithm validated in the study?",{"text":80,"@type":76},"Segmentation performance is evaluated on two synthetic datasets with an error of 2%, and the broader graph-based workflow is assessed using 3D simulation data with statistical and joint probability-density analyses.",{"name":82,"@type":73,"acceptedAnswer":83},"What do the results indicate about detonation cell geometry?",{"text":84,"@type":76},"The findings show oblong cells aligned with the wave propagation axis with 17% deviation, while dispersion in volume reflects cubic amplification of linear variability.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":22,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]